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MCQ (More than One Correct Answer)

### JEE Main 2016 (Online) 10th April Morning Slot

A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C ln (BD) holds true. Then which of the combination is not a meaningful quantity ?
A
A2 $-$ B2C2
B
${{\left( {A - C} \right)} \over D}$
C
${A \over B} - C$
D
${C \over {BD}} - {{A{D^2}} \over C}$

## Explanation

Given,

As log is dimensionless.

So, [BD] = 1   $\Rightarrow$  [B] = ${1 \over {\left[ D \right]}}$

Now checking options one by one

(a)   [B2 C2] = [B2] [A2 D2] = [A2] [B2 D2] = [A2]

$\therefore$   This is meaningful.

(b)   $\left( {{{A - C} \over D}} \right)$ is not meaningful.

As dimension of A $\ne$ dimension of C

Hence (A $-$ C)   is not possible.

(c)   $\left[ {{A \over B}} \right]$ = [AD] = [C]

$\therefore$   ${{A \over B}}$ $-$ C is meaningful.

(d)   $\left[ {{C \over {BD}}} \right]$ = ${{\left[ C \right]} \over {\left[ {BD} \right]}}$ = ${{\left[ C \right]} \over 1}$ = [C]

$\left[ {{{A{D^2}} \over C}} \right]$ = ${{\left[ {AD} \right]\left[ D \right]} \over {\left[ C \right]}}$ = ${{\left[ C \right]\left[ D \right]} \over {\left[ C \right]}}$ = [D]

As dimension of C and D are not same so it is not meaning ful.

#### Questions Asked from Units & Measurements

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JEE Main 2016 (Online) 10th April Morning Slot (1)
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